In this section we provide results for the mean-square end-to-end distance for a semiflexible polymer enclosed inside of a spherical domain. All the problem is reduced to solve the Neumann eigenvalue problem \(-\nabla ^2\psi =\lambda \psi \)  with Neumann boundary condition when the compact domain is \(\mathcal {B}:=\left\lbrace {\bf r}\in \mathbb {R}^{3}: {\bf r}^{2}\le R^{2}\right\rbrace \)  is a center ball of radius \(R\) . This problem is widely studied in different mathematical physics problems [1]}, [2]}. The eigenfunctions in this case can be given in terms of spherical Bessel functions \(j_{\ell }\left(x\right)\)  and spherical harmonic functions \(Y_{\ell m}\left(\theta , \varphi \right)\) ,
\(\psi _{\ell m k}\left(r, \theta , \varphi \right)=N_{\ell k}~j_{\ell }\left(\alpha _{\ell k}\frac{r}{R}\right)Y_{\ell m}\left(\theta , \varphi \right)\) 
